Problem: Vanessa is 8 years older than Gabriela. Three years ago, Vanessa was 5 times as old as Gabriela. How old is Gabriela now?
Explanation: We can use the given information to write down two equations that describe the ages of Vanessa and Gabriela. Let Vanessa's current age be $v$ and Gabriela's current age be $g$ The information in the first sentence can be expressed in the following equation: $v = g + 8$ Three years ago, Vanessa was $v - 3$ years old, and Gabriela was $g - 3$ years old. The information in the second sentence can be expressed in the following equation: $v - 3 = 5(g - 3)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $g$ , it might be easiest to use our first equation for $v$ and substitute it into our second equation. Our first equation is: $v = g + 8$ . Substituting this into our second equation, we get the equation: $(g + 8)$ $-$ $3 = 5(g - 3)$ which combines the information about $g$ from both of our original equations. Simplifying both sides of this equation, we get: $g + 5 = 5 g - 15$ Solving for $g$ , we get: $4 g = 20$ $g = 5$.